Remark 2 The design of the adaptive exploration-rate coefficients under DSSL significantly reduces the regret as compared to existing algorithms that use deterministic exploration-rate coefficients determined by the channel that requires the largest exploration time [1]}, [2]}, [3]}, [4]}. For example, consider the expected rate matrix \(U\)  given in Table REF , where parameter \(L\)  in (REF ) equals \(10^4\) . In Table REF , we present the deterministic exploration-rate coefficients \(D_{i,k}\)  defined in (REF ) for each channel-user pair under DSSL, where \(D_{i,k} \cdot \log (t)\)  is the number of samples required to achieve consistent estimates of the expected rates. By contrast, in other existing algorithms [1]}, [2]}, [3]}, [4]}, all channels are explored with the same exploration-rate coefficient, which is inversely proportional to the squared difference between the mean rate of the optimal allocation and the second best one. When applying this to our example, each channel should be explored for \(1600 \cdot \log (t)\)  time steps (as seen in Table REF ), which significantly increases the exploration times unnecessarily, and consequently increases the regret.

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